If \( f(x) \) is a function given by \( f(x)=\left|\begin{array}{lcc}\sin x & \sin a & \sin b \\...

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If \( f(x) \) is a function given by
\( f(x)=\left|\begin{array}{lcc}\sin x & \sin a & \sin b \\ \cos x & \cos a & \cos b \\ \tan x & \tan a & \tan b\end{array}\right| \), where \( 0ab\frac{\pi}{2} \)
Then the equation \( f^{\prime}(x)=0 \)
(A) has at least one root in \( (a, b) \)
(B) has at most one root in \( (a, b) \)
(C) has exactly one root in \( (a, b) \)
(D) has no root in \( (a, b) \)
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